Mr. Gove had been due to help shepherd Mr. Johnson’s leadership bid, but said that events since last Thursday’s referendum “have weighed heavily with me” and he had lost confidence in Mr. Johnson.

“I have come, reluctantly, to the conclusion that Boris cannot provide the leadership or build the team for the task ahead,” Mr. Gove said.

The referendum results plunged the country into uncertainty, prompting Prime Minister David Cameron to resign and opening up a political vacuum. The unexpected turn a week later represents another fracture in a Conservative Party that was already deeply divided over the referendum campaign, marking a break between two leaders on the Leave side.

The charismatic Mr. Johnson had been seen as having a strong claim to the job, and Mr. Gove had said previously that he didn’t want to be prime minister. Before his announcement, Mr. Johnson had been largely quiet in the week since the vote.

Mr. Johnson had been expected to announce his bid to lead the Conservatives, but said Thursday that “having consulted colleagues and in view of the circumstances of Parliament I have concluded that person cannot be me.”